How does one make it obvious that the structure of a neural network should be what it is?
While, as you begin to hit on, there are general guidelines to follow when building a neural network, they are far from standardized. This is because even though AI is a reasonably old field(1950s), neural networks have only been the tool of choice for less than a decade. Before, NNs did horribly, due to lack of data, and computation along with some less than efficient architectures. 

With that being said Hinton's general rule is to add nodes/layers till the model begins to overfit and then add dropout(pretty reasonable in practice).

As such, the whole field is essentially an art as much as a science currently with only basic guidelines to follow based on your problem and data. This is part of the beauty though imo, with there being so much left to discover.

Hope that helped answer your question!